Section 1 Lab Activity-1

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3090

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Statistics

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Apr 3, 2024

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STAT 3090 S ECTION 1 L AB A CTIVITY S PRING 2024 N AME : Megan McCauley P URPOSE : Some of the first questions we need to ask ourselves when confronted with inter- preting data are “Who or what is this data about?”, “Where did this data come from?”, What kind of data am I looking at?”. These initial questions will help us determine how to analyze and interpret the data. The following activity will help us practice answering these questions using the language specific to statistics. O BJECTIVES : Upon successful completion of this assignment, you will be able to… · Classify data into data types · Identify the population, sample, parameter, statistic in context · Determine if a statistic is being used for inference · Determine the type of study from the context of a problem · Distinguish between explanatory and response variables 1. Sleepy Hollow (40 pts) The town of Sleepy Hollow has 18,000 residents over the age of 10. We have recorded for us the number of hours generally slept per night by each resident over the age of 10. You will find this data by going to the website: https://www.rossmanchance.com/applets/2021/sampling/OneSample.html Be sure that the population data is for “Sleep 1”. Also, select “Show Sampling Options” on the right side. Realistically, it would be very difficult to record data for every person in this town. Thus, we would likely take a sample of the residents, calculate statistics from the sample data, and use those statistics as an educated guess for the actual population parameters of interest. We will use this data set to draw a sample of size 9 to illustrate several concepts of popu- lations, samples and data. a. What is the population? (4 pts) The population of the town of Sleepy Hollow is 18,000 people over the age of 10. b. Define at least two parameters that could be calculated from this population data. (4 pts) 1

STAT 3090 S ECTION 1 L AB A CTIVITY S PRING 2024 Mean (average number of hours slept by all residents over the age of 10), median number of hours slept by all residents over age 10 c. What is the value of the population mean (average)? Include units with your answer. (4 pts) 8.001 hours d. Is the value you listed in part c a parameter or a statistic? Explain. (4 pts) It’s a parameter because it is a numerical summary of the population. e. Take one sample of size 9. (4 pts) Under Sampling Options set the Number of samples to 1 and the Sample size to 9. Select Draw Samples . Record below the data values for your sample. Observation Value 1 8 2 4.5 3 8 4 9 5 8 6 8.25 7 8 8 9.75 9 5.50 f. What is the value of your sample mean? Include units. (4 pts) 7.667 hours 2

STAT 3090 S ECTION 1 L AB A CTIVITY S PRING 2024 g. Explain why the value calculated in part f is a statistic. (4 pts) It is a statistic because it was calculated from sample data. h. Use the table below to report the mean from 5 samples ( you can draw sample 5 times). (4 pts) Classmate Name: Mean P1 8.694 P2 8.667 P3 7.778 P4 8.194 P5 8.417 i. Compare your means to that of these five samples. Are the values the same of differ- ent? Why? (4 pts) They are different because each sample contains different elements of the population. j. The mean you found for your sample is an example of a descriptive statistic. How could you use this value for inference? (4 pts) We could use the sample mean as an estimate of the true population mean of the residents of Sleepy Hollow who are over the age of 10. 2. Stressed Out (21 pts) 3

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STAT 3090 S ECTION 1 L AB A CTIVITY S PRING 2024 Because of concerns about employee stress, a large company is conducting a study to compare two programs (tai chi or yoga) that may help employees reduce their stress lev- els. Tai chi is a 1200-year-old practice, originating in China, that consists of slow, fluid movements. Yoga is a practice, originating in India, that consists of breathing exercises and movements designed to stretch and relax muscles. The company has assembled a group of volunteer employees to participate in the study during the first half of their lunch hour each day for a 10-week period. Each volunteer will be assigned at random to one of the two programs. Volunteers will have their stress levels measured just before the beginning of the program and ten weeks later at the com- pletion of it. The difference in the two stress levels will be recorded. a. Identify the explanatory and response variables in the following study. Use a sen- tence or two to explain your choices. (7 pts) Explanatory Variable (independent variable): the type of program (yoga or tai chi). We will use the explanatory variable to help explain the change in stress lev- els. Response Variable (dependent variable): the difference between the volunteers’ stress levels at the beginning and end of the 10 weeks. We will see if this value depends on the type of program, making it a response variable. b. Would this study be considered an experiment or an observational study? Explain. (7 pts) Experiment; the volunteers are randomly assigned to one of the two programs. An in- terference is being used. c. How could you perform this study so that it is the other method from the one you se- lected in part b? (7 pts) We can let the volunteers pick their program instead of choosing it for them. 3. Complete in WebAssign the Section 1 assignment. (39 pts) 4

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